Effect of Pd for Rh substitution on thermoelectric power in the semimetallic compound URhGa5

Journal of Alloys and Compounds 584 (2014) 631–634

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom

Effect of Pd for Rh substitution on thermoelectric power in the semimetallic compound URhGa5 Ryszard Wawryk ⇑, Barbara Waszkiewicz, Zygmunt Henkie Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland

a r t i c l e

i n f o

Article history: Received 7 August 2013 Received in revised form 3 September 2013 Accepted 5 September 2013 Available online 16 September 2013 Keywords: URh0.97Pd0.03Ga5 Semimetals Thermoelectric power Electron doping Specific heat

a b s t r a c t Single crystals of URhGa5 and URh0.97Pd0.03Ga5 grown by the self-flux method were examined by X-ray diffraction, thermoelectric power, thermal and electrical conductivity, magnetization, and specific heat measurements. The giant thermoelectric peak exceeding 250 lV/K at 15 K observed for just grown URh0.97Pd0.03Ga5 crystals decreased drastically with ageing. Three percent palladium for Ru substitution in URhGa5 weakly changes the thermoelectric power beyond the peak area but substantially increases the electronic specific heat and magnetic susceptibility. The results of the diffusion thermoelectric power calculation, based on the electron structure and the Fermi surface literature data, are consistent with the determined data for URhGa5 crystal and its URh0.97Pd0.03Ga5 derivative. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Uranium compounds of the type UTGa5, where T is the transition atom, crystallize in the HoCoGa5-type tetragonal crystal structure (P4/mmm #123 D14h ) and represent one of the interesting series of ternary 115 compounds [1]. The superconductor PuCoGa5, with a high superconducting transition temperature Tsc = 18.5 K [2], and the heavy fermion superconductor CeCoIn5 (Tsc = 2.3 K) [3] also belong to the same 115 family. UTGa5 compounds order antiferromagnetically at low temperatures for T = Ni, Pd, and Pt or show low and almost temperatureindependent magnetic susceptibility, v, indicating Pauli-like paramagnetism, for T = Fe, Ru, Os, Co, Rh, and Ir [4]. De Haas-van Alphen examination revealed three kinds of small Fermi surface branches in UCoGa5 and URhGa5 with the volume of the largest one Va = 0.0059 VBZ (VBZ is the Brillouin zone volume), indicating that these compounds are semimetals [5]. The dHvA data do not show a clear relation between Va and the volumes of the two smaller branches for URhGa5. The electronic structure and Fermi surface calculation for UCoGa5 and URhGa5 also reveal that their Fermi surface consists of the small branches and show their positions in the Brillouin zone (BZ) [6]. We found a relatively high value of the thermoelectric power, S, for URhGa5, which leads to a value as high as 0.065 for the dimensionless thermoelectric figure of merit, ZT = S2T/qj (T, q, and j are temperature, electrical resistivity, and thermal conductivity) [7]. To find the origin of the high S ⇑ Corresponding author. Tel.: +48 713954303. E-mail address: [email protected] (R. Wawryk). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.09.039

and the possibility of enhancing it, the effect of electron doping on the thermoelectric power in URhGa5 has been realized. The electron structure and Fermi surface data of Refs. [5,6] and our estimation allowed us to predict the effect of electron doping of URhGa5 on its thermoelectric power. The predictions have been verified through doping with 0.03 electrons per BZ, which corresponds to the substitution of 3% of the Rh atoms by Pd ones, which exceed the number of carriers in the Va branch by a factor of 2.5. Thus we grew URhGa5 and URh0.97Pd0.03Ga5 single crystals, measured their thermoelectric power, electrical resistivity, specific heat, and magnetic susceptibility, and found their changes to be consistent with the electron doping of the considered band structure. This shows that the origin of the high S is the semimetallic electron structure of URhGa5; this feature, however, does not provide significant enhancement of the thermoelectric power by electron doping.

2. Experimental details Single crystals of URhGa5 and URh0.97Pd0.03Ga5 were grown by the self-flux method in the same way as the CeTIn5 compounds [8]. The grown crystals were washed in mercury at a temperature of about 80 °C for 24 h to remove a residual Ga-flux. Next the mercury was centrifuged, and then the rest of the Hg atoms were cleaned from the crystals in a high vacuum at a temperature of about 350 °C during 6 h. The X-ray powder diffraction revealed that the grown crystals of URh0.97Pd0.03Ga5 have the HoCoGa5-type crystal structure, the unit cell parameters are equal to a = 4.3023 Å and c = 6.8066 Å, and the unit cell volume Vu = 125.9887 Å3. In the limit of accuracy this Vu is consistent with a/c = 4.302/ 6.803 and Vu = 125.905 for URhGa5 [7] and a/c = 4.3195/6.8558 and Vu = 127.9161 for UPdGa5 [9]. The magnetic susceptibility was measured by a commercial SQUID magnetometer. Also, the specific heat was measured by a commercial set-up.

632

R. Wawryk et al. / Journal of Alloys and Compounds 584 (2014) 631–634

Samples of about (11.5)  (0.20.5)  (0.20.3) mm3 were cut from the crystals, then Cu electrical contacts (four points) were made by electrochemical deposition, and finally silver or gold thin wires were glued by silver paste for the electrical resistivity measurements, which were carried out in a 3He cryostat using an AC resistance bridge. A home-made set-up [10,11] was used for the thermoelectric power measurements. For the thermal conductivity examinations (under steady state conditions), the same S(T) measuring system was used with additional measurement of the electrical power supplied to heater generating temperature gradient in the sample.

3. Results 3.1. Thermoelectric power The temperature dependencies of the thermoelectric power for four samples of URh0.97Pd0.03Ga5 single crystals, labelled S1, S2, S3, and S4, are presented in Fig. 1. They are compared with S(T) data for URhGa5 (solid line) taken from Ref. [7]. There is a giant peak shown by S(T), which reaches the highest values of SMP = 250.7 lV/K at TMP = 15.3 K for sample S1 (open circles), 90 lV/K at TMP = 17.0 K for sample S2 (open triangles), and 17.7 lV/K at TMP = 25 K for sample S3 (open squares), respectively. Below TMP the thermoelectric power of all samples tends to zero for T ? 0, as expected. Above TMP, S(T) passes through a minimum at T  50–65 K and then increases up to broad maximum of 79 lV/ K at about 235 K (S1). The thermoelectric power of sample S1 was measured again after five months’ exposure to ambient air. A large reduction of the S(T) peak was observed. On the other hand, sample S3 was prepared from a crystal after seven months’ exposure to the air. The origin of the crystal ageing effect on the fall in the S(T) peak is to be determined. Finally, the reproducible results were obtained for samples S3 and S4. The latter sample was prepared from crystal that was re-annealed at a temperature of 350 °C. However, for the last sample a slightly higher SMP (19.6 lV/K) was observed. The S(T) dependence determined for URh0.97Pd0.03Ga5 along the c-axis (the dashed line in Fig. 1), as for the a-axis, passes the peak, reaching its maximum of 60 lV/K at TMP = 17.5 K and its minimum at about 50 K. The SMP value diminishes to 27 lV/K at TMP = 24 K when measured one year later (dash-dotted line). With increasing tempera-

Fig. 1. Thermoelectric power vs. temperature, S(T), for collections of S1 (open and filled circles, measured after growing and five months later, respectively), S2 (open triangles), S3 (open squares), and S4 (dotted curve) crystals of URh0.97Pd0.03Ga5 measured along the a-axis compared with S(T) data of URhGa5 (solid line) taken from [7] and of URh0.97Pd0.03Ga5 measured along the c-axis (after growing – dashed line; measured one year later – dash-dotted line). Left inset: Thermal conductivity of URh0.97Pd0.03Ga5 vs. temperature along the a-axis for sample S2 (diamonds) and sample S1 (filled circles) measured after five months. Right inset: Dimensionless thermoelectric figure of merit, ZT vs. temperature, for sample S2 (solid line) compared with the ZT for URhGa5 (dashed line) taken from Ref. [7].

ture, S exhibits a broad maximum of 65 lV/K at about TMb = 225 K. An enhancement of the dimensionless thermoelectric figure of merit, ZT, for sample S2 of URh0.97Pd0.03Ga5 is observed within limited ranges of temperature around TMP and TMb (right inset in Fig. 1). 3.2. Electrical resistivity The electrical resistivity, q, of URh0.97Pd0.03Ga5 and URhGa5 single crystals vs. temperature along the a- and c-axes is presented in Fig. 2. At low temperatures the q(T) of both compounds reveals the Fermi liquid-like behaviour; that is, q = q0 + AT2, where q0 and A for URh0.97Pd0.03Ga5 are, respectively, 7.39 lX cm and 0.00116 lX cm K2 along the a-axis and 5.92 lX cm and 0.00069 lX cm K2 along the c-axis. For URhGa5 these parameters are the same along the a- and c- axes and are equal to 11.0 lX cm and 0.00118 lX cm K2. They can be compared to values of 4.99 lX cm and 0.00156 lX cm K2, respectively, reported for the c-axis resistivity of URhGa5 [5]. The residual resistivity ratio, RRR (= q300K/q2K), is equal to 28 for the c-axis of URh0.97Pd0.03Ga5. As a result the transverse magnetoresistivity, MR, of this crystal is equal to 180–400% below 25 K (the inset in Fig. 2), which points to a high mobility of the current carriers in this region, where the anomalous peak of thermoelectric power is observed. It is worth noticing that the giant peak of S(T), which declines with a lapse of crystal time, is related to the unusual Pd doping effect; that is, doping of URhGa5 with 3 at.% Pd increases the RRR and the carrier mobility in the peak region of temperature. 3.3. Specific heat The specific heat, Cp, vs. T of URhGa5 and URh0.97Pd0.03Ga5 single crystals measured at low T is presented in Fig. 3. The data for 0.4 K 6 T 6 5 K can be fitted well with the standard expression:

C p ¼ cT þ bT 3

ð1Þ 2

for the electronic specific heat coefficient c = 5.9 mJ/K mol and parameter b = 7.68  104 J/K4 mol for URhGa5 (see the inset in Fig. 3). For URh0.97Pd0.03Ga5 the corresponding data are equal: c = 7 mJ/K2 mol and b = 3.21  104 J/K4 mol. The b parameters result in Debye temperatures HD equal 261 K for URhGa5 and

Fig. 2. Electrical resistivity vs. temperature for the a- (solid line) and c-axes (dashed line) of URhGa5 as well as for the a- (dash–dot line) and c-axes (dash–dot–dot line) of URh0.97Pd0.03Ga5. The dotted line presents the q(T) for URh0.97Pd0.03Ga5 along the c-axis in a magnetic field of 9 T. Inset: Transverse magnetoresistivity, MR, vs. temperature along the a- and c-axes of URh0.97Pd0.03Ga5.

R. Wawryk et al. / Journal of Alloys and Compounds 584 (2014) 631–634

633

3.4. Magnetic susceptibility

Fig. 3. Specific heat of URhGa5 (triangles, dotted) and URh0.97Pd0.03Ga5 (circles, dotted) single crystals vs. temperature measured at low temperatures. The dashed lines 1 and 2 present the Cp(T) data fitted to Eq. (1) for URhGa5 and URh0.97Pd0.03Ga5, respectively. The solid line presents the fit of the Cp(T) data to Eq. (2) for URh0.97Pd0.03Ga5. Inset: the Cp/T vs. T2 dependencies.

349 K for URh0.97Pd0.03Ga5. The determined here data for URhGa5 can be compared with that reported in the literature, c = 5.4 mJ/ K2 mol and HD = 390 K [5]. Dashed curves 1 and 2 in the main part of Fig. 3 show the Cp(T) dependence resulting from Eq. (1) extended to higher temperatures for URhGa5 and URh0.97Pd0.03Ga5, respectively, for which the parameters were determined for T 6 5 K. The calculated curve 1 fits well to experimental data of URhGa5 up to T = 10.5 K, while the calculated curve 2 deviate from the experimental Cp(T) data for URh0.97Pd0.03Ga5 above 7 K. Therefore we have tried to fit of the specific heat by the Debye and Einstein model together, based on Ref. [12], as described below:

C p ðTÞ ¼ C el þ C ph ¼ cT þ qD C D þ qE C E ;

ð2Þ

where CD and CE are specific heats originating from the Debye and Einstein models, respectively:

C D ¼ 9NkB ðT=HD Þ3

Z

HD =T

0

¼ 3NkB

eHE =T ðHE =TÞ2 ðeHE =T  1Þ

ex x4 ðex

2

;

 1Þ2

dx;

The data for magnetic susceptibility, v(T), in magnetic field B = 0.1 T are shown in Fig. 4 for URhGa5 and URh0.97Pd0.03Ga5 crystals measured along the [1 0 0] and [0 0 1] directions. For both compounds, v shows a weak and unusual T dependence and a distinct anisotropy. The roughly temperature-independent v(T) at the lowest temperatures increases with temperature at a rate of about 106 cm3/mol K for the a- axis and at a rate two times higher along the c- direction. In the latter case there is also a small upturn in v(T) for T ? 0 and it approaches saturation or its maximum value above 400 K. The v(T) data for URh0.97Pd0.03Ga5 are shifted up by 0.13  and 0.6  103 cm3/mol K for the a- and c-axes, respectively, compared to v(T) for the parent compound. Similar behaviour of v(T) as for the c-axis in URh0.97Pd0.03Ga5 and URhGa5 was observed for other compounds such as U2RuGa8 [13] and ceriumfilled skutterudites CeOs4As12 [14], CeRu4As12 [15], and CeFe4As12 [16], where such behaviour was interpreted in terms of the intermediate valence or the Kondo lattice picture [14].

4. Discussion The de Haas-van Alphen examination of UCoGa5 revealed three branches of the Fermi surface named a, b, and c having volumes of Va = 0.0059 VBZ, Vb = 0.0028 VBZ, and Vc = 0.0030 VBZ with cyclotron masses mc ðm0 Þ known for all branches for cyclotron orbits perpendicular to the [0 0 1] axis and equal to 0.82, 1.74, and 2.93, respectively [5]. We have assume that the carriers density of the Fermi branches can be described by parabollic bands for which the effective masses of the density of states are assumed to be equal to those of the cyclotron masses in the ab plane. Using handbook formulas we estimated the 0 K individual Fermi energies of particular branches EF,i for carrier densities na = 9.37  1019 e/cm3, nb = 4.45  1019 e/cm3, and nc = 4.77  1019 e/cm3, which are equal to EF,a = 0.0918 eV, EF,b = 0.0263 eV, and EF,c = 0.0164 eV, respectively. This means that metallic approximation works well at low temperatures, where the impurity scattering may however limit the accuracy. Therefore we compared our calculated data for the thermoelectric power with the experimental ones determined for temperatures of 50 and 100 K.

CE ð3Þ

qD and qE are the vibration modes for r = 7 atoms, N is the Avogadro number, kB is the Boltzmann constant, HE is the Einstein temperature, and x = ⁄xD/kBT. For simplicity we used only one Einstein mode. With seven atoms per molecule of URh0.97Pd0.03Ga5, there are in total qph = 3  7 = 21 phonon modes: three acoustic and eighteen optical modes. The solid line in Fig. 3 presents result of fitting the Cp(T) data of URh0.97Pd0.03Ga5 to Eq. (2) for 0.4 6 T 6 20 K. From the fitting one obtains c = 7 mJ/K2 mole, qD = 11.71, and qE = 9.29, and consequently the Debye and Einstein temperatures equals to 220 K and 116 K, respectively. The Einstein and Debye model together described the experimental data very well above 9 K and very poorly below. Also the Cp(T) data for URhGa5 can be hardly fitted by the Einstein and Debye model together. The Pd3+ ion has one more valence electron and a radius about 10% larger compared to Rh3+. Therefore substitution of Pd for 3% of the Rh in URhGa5 substantially enhances the electronic specific heat coefficient c and changes spectrum of vibration modes.

Fig. 4. Magnetic susceptibility vs. temperature for URhGa5 crystal measured in a magnetic field parallel to the [1 0 0] direction (filled circles) and for B parallel to [0 0 1] axis (open circles) as well as for URh0.97Pd0.03Ga5 crystals in B parallel to the [1 0 0] axis (filled squares) and for B parallel to the [0 0 1] direction (open triangles) in fields B = 0.1 T.

634

R. Wawryk et al. / Journal of Alloys and Compounds 584 (2014) 631–634

When the diffusion thermoelectric power S(T) arises from the simultaneous action of several Fermi branches it is given by [17]:

SðTÞ ¼

n X i¼1

Si ðTÞPi ðTÞ; ,

¼ ri ðTÞ

n X

2

Si ðTÞ ¼ xðp2 kB TÞ=3qi EF;i ;

ri ðTÞ;

Pi ðTÞ ð4Þ

i¼1

where the subscript i labels the Fermi branch, Pi(T) is the fraction of the total conductivity contributed by the i-th branch, and Si(T) is the diffusion thermoelectric power that one would calculate if the i-th band were to contribute. For the calculation we take P Pi ðTÞ ¼ ni li = ni¼1 ni li and li =lj  ðmj =mi Þ2:5 [18]. The symbols qi, ni, and li are the charge, number, and mobility of carriers of the ith branch, with mobility la, lb = 0.152 la, and lc = 0.0414 la, respectively. The temperature-independent x parameters between 2 and 3 [19] were observed for various simple metals. The electronic structure and Fermi surface calculation for UCoGa5 and URhGa5 revealed four identical small electron sheets of the Fermi surface in the 16th band inside and small hole sheets in the 15th band – one in the centre of the BZ, two on the BZ walls (in the [1 0 0] and [0 1 0] directions), and four very small sheets inside the 15th BZ (we call them Vd branches) [6]. We expect that the charge of the 4  Vc electron sheets will compensate 1  Va + 2  Vb + 4  Vd hole sheets, where Vd = 0.000125 has to be assumed for carrier charge compensation but is experimentally undetected. Calculation of the thermoelectric power, Sc, for such a Fermi band structure results in thermoelectric power Sc(50 K)/Sc(100 K) equal to 11x/22x and 10x/20x (in lV K1) for URhGa5 and URh0.97Pd0.03Ga5, respectively, while the experimental data for S(50 K)/S(100 K) are equal to 11/ 33.5 and 11.5/26 (in lV K1), respectively. Good consistency between the calculated and experimental data for the thermoelectric power is reached for a ‘‘scattering parameter’’ x equal to 1 rather than 2 or 3. But it seems more important that the calculation correctly predict the observed weak effect of electron doping on thermoelectric power. This allows us to understand the origin of the experimentally observed weak effect of 3% Pd for Rh substitution in URhGa5 on its thermoelectric power. It should be mentioned here that in this range of temperatures, namely from 50 to 100 K, the significant difference between experimental values of thermoelectric power for URhGa5 and URh0.97Pd0.03Ga5 is not observed. A larger difference in the S values was found below 50 K and above 150 K (Fig. 1). Because of the high effective masses of Vc branch carriers (electrons), the four Vc branches consume as many as 76% of the number of doped electrons but contribute only by 15% of their negative value to the thermoelectric power. On the other hand, the light effective mass carriers (holes) of Va branch consumes merely about 6% of the doped electrons reducing the number of its holes, but contributes even by 78% in its positive thermoelectric power to the total one. The two Vb branches complete the lacking carrier and thermoelectric power contributions. This explains the weak sensitivity of thermoelectric power to doping of URhGa5 semimetal with the number of electrons being of the same order as the

number of carriers from the Fermi branches. It is worth noticing that dominant consumption of the doped electrons by the heavy mass branches is consistent with substantial increases in the magnetic susceptibility and the electronic specific heat coefficient with the examined doping. In summary, we have measured and analyzed the temperature dependencies of the thermoelectric power, electrical resistivity, specific heat, and magnetic susceptibility of the single crystals of both URh0.97Pd0.03Ga5 and its parent compound URhGa5. The observed giant peak in the S(T) dependence at low-T just after growing the former crystal, has then been reduced drastically with passing a time. An electron doping realized by the substitution of 3% Rh by Pd have influenced on the thermoelectric power at low-T and above 150 K up to room temperatures and caused an increase in the values of the electronic specific heat and magnetic susceptibility. Acknowledgements The authors are indebted to E. Bukowska for the X-ray measurements and to R. Gorzelniak for his assistance with the magnetic susceptibility examinations. References [1] Yu.N. Grin, P. Rogl, K. Hiebl, J. Less-Common Met. 121 (1986) 497–505. [2] J.L. Sarrao, L.A. Morales, J.D. Thomson, N.J. Curro, Bull. Am. Phys. Soc. 47 (2002) 164. [3] C. Petrovic, P.G. Pagliso, M.F. Hundley, R. Movshovich, J.L. Sarrao, J.D. Thomson, Z. Fisk, P. Montoux, J. Phys. Condens. Matter 13 (2001) L337–L342. [4] S. Ikeda, Y. Tokiwa, T.D. Matsuda, A. Galatanu, E. Yamamoto, A. Nakamura, Y. ¯ nuki, Physica B 359–361 (2005) 1039–1041. Haga, Y. O ¯ nuki, [5] S. Ikeda, Y. Tokiwa, T. Okubo, Y. Haga, E. Yamamoto, Y. Inada, R. Settai, Y. O J. Nucl. Sci. Technol. Suppl. 3 (2002) 206–209. [6] T. Maehira, M. Higuchi, A. Hasegawa, (2002).; T. Maehira, M. Higuchi, A. Hasegawa, Physica B 329–333 (2003) 574–575. [7] R. Wawryk, Z. Henkie, T. Cichorek, C. Geibel, F. Steglich, Phys. Stat. Sol. (b) 232 (2002) R4–R6. [8] E.G. Moshopoulou, Z. Fisk, J.L. Sarrao, J.D. Thomson, J. Solid State Chem. 158 (2001) 25–33. [9] S. Ikeda, T.D. Matsuda, Y. Haga, E. Yamamoto, M. Nakashima, S. Kirita, T.C. Kobayashi, M. Hedo, Y. Uwatoko, H. Yamagami, H. Shishido, T. Ueda, R. Settai, ¯ nuki, J. Phys. Soc. Jpn. 74 (8) (2005) 2277–2281. Y. O [10] Z. Henkie, R. Wawryk, Solid State Commun. 122 (2002) 1–6. [11] R. Wawryk, Z. Henkie, Philos. Mag. B 81 (2001) 223–234. [12] A.P. Ramirez, G.R. Kowach, Phys. Rev. Lett. 80 (1998) 4903–4906. [13] R. Troc´, Z. Bukowski, C. Sułkowski, J.A. Morkowski, A. Szajek, G. Chełkowska, Physica B 359–361 (2005) 1375–1377. [14] R.E. Baumbach, P.-C. Ho, T.A. Sayles, M.B. Maple, R. Wawryk, T. Cichorek, A. Pietraszko, Z. Henkie, PNAS 105 (2008) 17307–17311. [15] R.E. Baumbach, P.-C. Ho, T.A. Sayles, M.B. Maple, R. Wawryk, T. Cichorek, A. Pietraszko, Z. Henkie, J. Phys.: Condens. Matter 20 (2008) 075110–1–7. [16] R. Wawryk, Z. Henkie, A. Pietraszko, T. Cichorek, L. Ke˛pin´ski, A. Jezierski, J. Kaczkowski, R.E. Baumbach, M.B. Maple, Phys. Rev. B 84 (2011) 165109–1–11. [17] F.J. Blatt, P.A. Schroeder, C.L. Foiles, D. Greig, Thermoelectric Power of Metals, Plenum Press, New York and London, 1976. p. 152. [18] E. Burstein, P.H. Egli, The Physics of Semiconductor Materials, in: L. Marton (Ed.), Advances in Electronics and Electron Physics, vol. VII, Academic Press Inc., New York, 1955, p. 69. [19] N. Cusack, The Electrical and Magnetic Properties of Solids, Longmans, Green and Company Ltd., London, 1958. p. 116.